In [1]:
from numpy import *
In [ ]:
from euler import product
In [2]:
a = array([
[ 8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
[22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
[ 4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
[ 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
[ 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48],
])
In [3]:
n = 4
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a[2, 3]
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In [5]:
a[(2, 3)]
Out[5]:
In [6]:
a[2, 3:3+n]
Out[6]:
In [7]:
a[2:2+n, 3]
Out[7]:
In [9]:
%timeit product(range(1, 100))
product(range(1, 100))
Out[9]:
In [10]:
import operator
def product(x):
return reduce(operator.mul, x)
In [11]:
%timeit product(range(1, 100))
product(range(1, 100))
Out[11]:
In [12]:
product(a[2:2+n, 3])
Out[12]:
In [13]:
a.shape
Out[13]:
In [14]:
[i + 2 * n for i in a.shape]
Out[14]:
In [15]:
aa = zeros([i + 2 * n for i in a.shape], dtype=int)
aa[n:n+a.shape[0], n:n+a.shape[1]] = a
print aa[4, 4]
print aa[(4, 4)]
In [16]:
def make_directions():
directions = set([])
for dir in [(x, y) for x in (1, 0, -1) for y in (1, 0, -1)]:
if dir == (0, 0):
continue
if (-dir[0], -dir[1]) not in directions:
directions.add(dir)
return directions
In [17]:
make_directions()
Out[17]:
In [18]:
def foo(n):
max_product = 0
if True:
for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):
max_product = max(
max_product,
product(aa[p[0], p[1]:p[1]+n]),
product(aa[p[0]:p[0]+n, p[1]]))
return max_product
In [19]:
%timeit foo(n)
foo(n)
Out[19]:
In [20]:
def foo(n):
max_product = 0
for dir in make_directions():
dir = array(dir)
for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):
q = product([aa[tuple(p + i * dir)] for i in range(n)])
# print p, q
if q > max_product:
max_product = q
return max_product
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%timeit foo(n)
foo(n)
Out[21]:
In [22]:
def foo(n):
max_product = 0
for dir in make_directions():
dir = array(dir)
for p in ((x, y) for x in xrange(n, n+a.shape[0]) for y in xrange(n, n+a.shape[1])):
max_product = max(max_product,
product([aa[tuple(p + i * dir)] for i in range(n)]))
return max_product
In [23]:
%timeit foo(n)
foo(n)
Out[23]: